A number of phase shifting interferometer designs (as well as other types of interferometer designs used for measuring distances) are intended to provide 2 quadrature signals, ideally orthogonal output signals V1 ideal and V2 ideal as shown by EQUATIONS 1 and 2 below:                                           V            1                    ⁢          ideal                =                  Sin          ⁢                                    2              ⁢                                                          ⁢              π                        λ                    ⁢          z                                    (                  Eq          .                                          ⁢          1                )                                                      V            2                    ⁢          ideal                =                  Cos          ⁢                                    2              ⁢                                                          ⁢              π                        λ                    ⁢          z                                    (                  Eq          .                                          ⁢          2                )            where λ is the wavelength of radiation used in the interferometer and z is the optical pathlength difference (OPD) between the interfering test object path light beam and reference path light beam. These two quadrature input signals of an interferometer should ideally both arise from light coming from precisely the same portion of the test object. The OPD z for that portion of the test object can then be determined to high resolution within a particular wavelength from EQUATION 3, which is described herein as providing “signal interpolation” for the value of z, or an “interpolated” value for z, or an interpolated interferometer measurement, within a particular wavelength:                     z        =                              λ                          2              ⁢                                                          ⁢              π                                ⁢                      Tan                          -              1                                ⁢                                                                      V                  1                                ⁢                ideal                                                              V                  2                                ⁢                ideal                                      .                                              (                  Eq          .                                          ⁢          3                )            
However, in practical interferometers, the output signals are better described by the general forms shown in EQUATIONS 4 and 5:                               V          1                =                              C            1                    +                                    A              1                        ⁢            Sin            ⁢                                          2                ⁢                                                                  ⁢                π                            λ                        ⁢            z                                              (                  Eq          .                                          ⁢          4                )                                          V          2                =                              C            2                    +                                    A              2                        ⁢            Cos            ⁢                                          2                ⁢                                                                  ⁢                π                            λ                        ⁢            z                                              (                  Eq          .                                          ⁢          5                )            
Where C1 and C2 are offset or “DC” components in the signals and A1 and A2 are the “AC” signal amplitudes. The offset components of the signals arise from a number of sources. For example, a primary contribution comes from the nominal DC intensity of each of the interfering light beams that contribute to each interferometer output signal. This will vary with the intensity of the laser source, for example. Furthermore, it should be appreciated that a primary cause of variations in the nominal DC intensity of the object beams, or portions of the object beams, is that there are generally variations in the effective reflectivity of any particular portion of the test object. Similar effects may arise in the reference beams as well. However, the reflectivity of the reference mirror is generally more uniform, and more stable, than that of the various “uncontrolled” test objects. Additional contributions to offset arise from various ambient light contributions, as well as offsets associated with the detectors and the associated signal conditioning electronics and the like used to detect and measure the signals V1 and V2, for example.
Thus, even if A1=A2, if offsets are present in the signals, the signals depart from the form expected in EQUATION 3, and the resulting interpolated z values include related errors. Thus, for high accuracy interpolation, it is necessary to eliminate or compensate the offsets prior to computation of the interpolated value.
A number of different methods have been designed for eliminating or compensating such offsets in phase shifting interferometers. For example, U.S. Pat. No. 6,304,330, which is incorporated herein by reference for all of its relevant teachings, discloses a novel multiple phase-shifting image generating structure that combines a wavefront-spreading element, a phase-shifting interference element and a sensing element. By combining the wavefront-spreading element, the phase-shifting interference element, and the sensing element, the multiple phase-shifting image generating structure shown in the '330 patent is able to convert many sources of potential error in interferometry measurements, including some contributors to signal offset components, into common-mode errors. That is, these errors, in view of the signals provided by the multiple phase-shifting image generating structure disclosed in the '330 patent, equally affect multiple measurement signals provided in that system. As a result, the magnitude and direction of these common-mode errors can be determined and substantially eliminated by properly processing the interferometry signals provided by the multiple phase-shifting image generating structure disclosed in the '330 patent.
However, the structure and methods of the '330 patent, as well as other known prior art methods for eliminating or compensating offset errors, generally require either additional optical paths or means for introducing precisely controlled path length variations, as well as the associated additional components, in order to provide the required signals. Furthermore, residual sources of offset error generally remain in known prior art systems. Thus, systems and methods that could overcome the foregoing disadvantages, separately, or in combination, would be desirable.